Graphene membrane components are frequently used in microelectromechanical systems (MEMS). It can be desirable here to have a tensioned graphene membrane in a graphene membrane component. For example, U.S. Patent Application Publication No. 2013/0062104 A1 discloses a resonant structure and a process for the production of the resonant structure. The resonant structure includes a substrate and at least one cavity. In another example, German Patent Application No. DE 10 2014 204 712 A1 discloses an acoustic transducer which is an MEMS. A microphone with a graphene membrane is moreover disclosed.